Question

Plasma volume is an indicator of overall health of a person. A random sample of 41 firefighters are tested and have an average plasma volume of 35. It is known that the population standard deviation is 8. Construct a 99% confidence interval for the population mean blood plasma volume in male firefighters. Point Estimate: = Margin of Error: E = (round to 4 decimal places) Lower Limit: (round to 4 decimal places) Upper Limit: (round to 4 decimal places) We are % confident that the true is between and . For help, view video.

Answer 1

Margin of Error = 3.0250

99% Confidence interval for the population mean of blood plasma volume in male firefighters = (31.9750, 38.0250)

We are 99% confident that the true population mean of blood plasma volume in male firefighters is in the range (31.9750, 38.0250)

Explanation:

Confidence interval gives a range of values where the mean can be obtained with a certain level of confidence.

Confidence interval = (Sample mean) ± (Margin of error)

Sample mean = 35

Margin of Error = (critical value) × (standard deviation of the distribution of sample means)

Critical value

For the critical value, we will use the t-distribution with a significance level of (0.01/2) and degree of freedom = 41 - 1

α = 0.005

df = 40

t = 2.42 (this is the t-score value, we used the t-distribution because the standard deviation and the mean for the population isn't known)

Standard deviation of the distribution of sample means = σ/√n

where σ = Sample standard deviation = 8

n = sample size = 41

Standard deviation of the distribution of sample means = (8/√41) = 1.25

Margin of error = 2.420 × 1.25 = 3.0250

Confidence interval = (Sample mean) ± (Margin of error) = 35 ± 3.0250

Confidence interval = (31.9750, 38.0250)

Hope this Helps!!!